the quadratic equation 3x^2-7x=3 has roots that are...1.)real, rational, and equal 2.)real, rational and unequal 3.)real, irrational and unequal...

Given the quadratic
equation:

3x^2 - 7x =
3

==> 3x^2 - 7x -3 =
0

We need to determine the type of
roots.

Then, we will use the discriminant to find
out.

We know that:

delta = b^2
- 4ac

If delta = 0 ==> then the equation has one
real root.

If delta > 0 ==> then the equation
has two real roots.

If delta < 0 then the equation
has two complex roots.

If delta is a complete square, then
it has 2 rational roots

If delta is not a complete square,
then it has 2 irrational roots.

Let us test
delta.

delta = b^2 -4ac = (-7)^2 - 4*3*-3 = 49 + 36 =
85

Then delta > 0 , then it has two real
roots.

Also, delta is NOT a complete square, then it has
irrational roots.

Then, the answer is number
(3) Real, irrational, and unequal.